A novel hierarchical multi-mode molecular stress function (HMMSF) model for long-chain branched (LCB) polymer melts is proposed, which implements the basic ideas of (i) the pom-pom model, (ii) hierarchal relaxation, (iii) dynamic dilution, (iv) interchain pressure and (v) convective constraint release relaxation mechanism. Here, the capability of this approach is demonstrated in modelling the steady shear data of a broadly distributed long-chain branched polymer melt with only two non-linear parameters, a dilution modulus and a convective constraint release (CCR) parameter.